The nonexistence of expansive \(\mathbb Z^n\) actions on Peano continua that contain no \(\theta\)-curves

DOI10.1016/J.TOPOL.2006.06.005zbMath1112.54013OpenAlexW2013992704MaRDI QIDQ864466

Youcheng Zhou, Li Zhen Zhou, En Hui Shi

Publication date: 9 February 2007

Published in: Topology and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.topol.2006.06.005

zbMATH Keywords

continuumgroup actionexpansiveness\(\theta\)-curveDendrite

Mathematics Subject Classification ID

Continua theory in dynamics (37B45) Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.) (37B05)

Related Items (4)

Unnamed Item ⋮ The nonexistence of sensitive commutative group actions on dendrites ⋮ The nonexistence of sensitive commutative group actions on graphs ⋮ The nonexistence of expansive commutative group actions on Peano continua having free dendrites

Cites Work

• The nonexistence of expansive homeomorphisms of Peano continua in the plane
• A direct proof that each Peano continuum with a free arc admits no expansive homeomorphisms
• The Nonexistence of Expansive \(\mathbb Z^d\) actions on graphs
• The nonexistence of expansive homeomorphisms on a closed 2-cell
• Each compact orientable surface of positive genus admits an expansive homeomorphism
• A Note on Unstable Homeomorphisms
• The nonexistence of expansive homeomorphisms of dendroids
• The Nonexistence of Expansive Homeomorphisms of 1-Dimensional Compact ANRS
• Tree-like continua do not admit expansive homeomorphisms
• Refinable maps in the theory of shape
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